17. the circumference of $\odot i$ is $21\pi$. find $nx$.
18. the circumference of $\odot a$ is $36\pi$. find $va$.
19. $m\widehat{an} = 32^{\circ}$ and $m\widehat{nf} = 94^{\circ}$. find $m\widehat{af}$.
20. $m\widehat{op} = 37^{\circ}$. find $m\widehat{ps}$.
21. the circumference of $\odot i$ is $22\pi$. find $ih$.
22. $rn = 18$. find $ra$.
23. the circumference of $\odot i$ is $16\pi$. find $ht$.
24. $m\widehat{fkn} = 168^{\circ}$, $m\widehat{uf} = 34^{\circ}$. find $m\widehat{un}$.

Question

Accepted Answer

{ "quality": "clear", "question_count": 8, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Circle Circumference", "Circle Radius and Diameter", "Arc Measure" ], "new_concepts": [ "Circle Chord Properties" ], "current_concepts": [ "Circle Circumference", "Circle Radius and Diameter", "Arc Measure", "Circle Chord Properties" ] } The image is oriented upside down. Let's first read and analyze each question by rotating the content mentally by 180 degrees. Looking at the rotated questions: ## Question 17 - Text: "17. The circumference of $\odot I$ is $21\pi$. Find $NX$." - Diagram: A circle with center $I$ and a segment $NX$ passing through the center $I$. Thus, $NX$ is a diameter. - Using the **Circle Circumference** and **Circle Radius and Diameter** knowledge points: Using the *Circle Circumference* and *Circle Radius and Diameter* knowledge points $$ C = \pi d \implies 21\pi = \pi \cdot NX \implies NX = 21 $$ ## Question 18 - Text: "18. The circumference of $\odot A$ is $36\pi$. Find $VA$." - Diagram: A circle with center $A$ and a segment $VA$ from the center $A$ to the boundary. Thus, $VA$ is a radius. - Using the **Circle Circumference** and **Circle Radius and Diameter** knowledge points: Using the *Circle Circumference* and *Circle Radius and Diameter* knowledge points $$ C = 2\pi r \implies 36\pi = 2\pi \cdot VA \implies VA = 18 $$ ## Question 19 - Text: "19. $m\widehat{AN} = 32^\circ$ and $m\widehat{NF} = 94^\circ$. Find $m\widehat{AF}$." - Diagram: A circle with points $A$, $N$, and $F$ on the boundary. The arc $AF$ is composed of adjacent arcs $AN$ and $NF$. - Using the **Arc Measure** knowledge point: Using the *Arc Measure* knowledge point $$ m\widehat{AF} = m\widehat{AN} + m\widehat{NF} = 32^\circ + 94^\circ = 126^\circ $$ ## Question 20 - Text: "20. $m\widehat{OP} = 37^\circ$. Find $m\widehat{PS}$." - Diagram: A circle with center $T$ and diameter $OS$. Point $P$ lies on the circle. Since $OS$ is a diameter, the arc $OPS$ is a semicircle, which measures $180^\circ$. - Using the **Arc Measure** knowledge point: Using the *Arc Measure* knowledge point $$ m\widehat{PS} = 180^\circ - m\widehat{OP} = 180^\circ - 37^\circ = 143^\circ $$ ## Question 21 - Text: "21. The circumference of $\odot I$ is $22\pi$. Find $IH$." - Diagram: A circle with center $I$ and radius $IH$. - Using the **Circle Circumference** and **Circle Radius and Diameter** knowledge points: Using the *Circle Circumference* and *Circle Radius and Diameter* knowledge points $$ C = 2\pi r \implies 22\pi = 2\pi \cdot IH \implies IH = 11 $$ ## Question 22 - Text: "22. $RN = 18$. Find $RA$." - Diagram: A circle with center $A$ and diameter $RN$. Thus, $RA$ is a radius. - Using the **Circle Radius and Diameter** knowledge point: Using the *Circle Radius and Diameter* knowledge point $$ RA = \frac{RN}{2} = \frac{18}{2} = 9 $$ ## Question 23 - Text: "23. The circumference of $\odot I$ is $16\pi$. Find $HT$." - Diagram: A circle with center $I$ and diameter $HT$. - Using the **Circle Circumference** and **Circle Radius and Diameter** knowledge points: Using the *Circle Circumference* and *Circle Radius and Diameter* knowledge points $$ C = \pi d \implies 16\pi = \pi \cdot HT \implies HT = 16 $$ ## Question 24 - Text: "24. $m\widehat{FKN} = 168^\circ$, $m\widehat{UF} = 34^\circ$. Find $m\widehat{UN}$." - Diagram: A circle with points $F$, $K$, $N$, and $U$ on the boundary. The entire circle is $360^\circ$. The circle is divided into major arc $\widehat{FKN}$ and arc $\widehat{FNU}$ (which consists of $\widehat{UN}$ and $\widehat{UF}$). - Using the **Arc Measure** knowledge point: Using the *Arc Measure* knowledge point $$ m\widehat{FKN} + m\widehat{UF} + m\widehat{UN} = 360^\circ \implies 168^\circ + 34^\circ + m\widehat{UN} = 360^\circ \implies m\widehat{UN} = 158^\circ $$ | No. | Problem | Answer | |---|---|---| | 17 | The circumference of $\odot I$ is $21\pi$. Find $NX$. | $21$ | | 18 | The circumference of $\odot A$ is $36\pi$. Find $VA$. | $18$ | | 19 | $m\widehat{AN} = 32^\circ$ and $m\widehat{NF} = 94^\circ$. Find $m\widehat{AF}$. | $126^\circ$ | | 20 | $m\widehat{OP} = 37^\circ$. Find $m\widehat{PS}$. | $143^\circ$ | | 21 | The circumference of $\odot I$ is $22\pi$. Find $IH$. | $11$ | | 22 | $RN = 18$. Find $RA$. | $9$ | | 23 | The circumference of $\odot I$ is $16\pi$. Find $HT$. | $16$ | | 24 | $m\widehat{FKN} = 168^\circ$, $m\widehat{UF} = 34^\circ$. Find $m\widehat{UN}$. | $158^\circ$ | { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Geometry", "Circle Circumference" ] }

No.	Problem	Answer
18	The circumference of \(\odot A\) is \(36\pi\). Find \(VA\).	\(18\)
19	\(m\widehat{AN} = 32^\circ\) and \(m\widehat{NF} = 94^\circ\). Find \(m\widehat{AF}\).	\(126^\circ\)
20	\(m\widehat{OP} = 37^\circ\). Find \(m\widehat{PS}\).	\(143^\circ\)
21	The circumference of \(\odot I\) is \(22\pi\). Find \(IH\).	\(11\)
22	\(RN = 18\). Find \(RA\).	\(9\)
23	The circumference of \(\odot I\) is \(16\pi\). Find \(HT\).	\(16\)
24	\(m\widehat{FKN} = 168^\circ\), \(m\widehat{UF} = 34^\circ\). Find \(m\widehat{UN}\).	\(158^\circ\)

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22

Question 23

Answer: